|
%I #19 Sep 08 2022 08:44:40
%S 1,61083979321,4264288605349394427001,
%T 292468454161371994489927453227641,
%U 20103187136428193301141459556344509715532409,1381438342588687480407961010312719764427906885156653689,94932082182896025238148883982319050364413593497347296287825382009
%N Gaussian binomial coefficient [ n,12 ] for q=-8.
%D J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H Vincenzo Librandi, <a href="/A015431/b015431.txt">Table of n, a(n) for n = 12..100</a>
%F a(n) = Product_{i=1..12} ((-8)^(n-i+1)-1)/((-8)^i-1) (by definition). - _Vincenzo Librandi_, Nov 06 2012
%t Table[QBinomial[n, 12, -8], {n, 12, 20}] (* _Vincenzo Librandi_, Nov 06 2012 *)
%o (Sage) [gaussian_binomial(n,12,-8) for n in range(12,17)] # _Zerinvary Lajos_, May 28 2009
%o (Magma) r:=12; q:=-8; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 06 2012
%K nonn,easy
%O 12,2
%A _Olivier Gérard_
|
